Methods
to identify complex features that are present in fisheries analysis because of their ability 85
to learn nonlinear and complex patterns. Neural networks penalize complexity differently from 86
GLMs by the progressive updating of model weights (Fan et al., 2021), and can optionally set a 87
subset of model weights to zero to prevent overfitting (Srivastava et al., 2014). These approaches 88
are known as “implicit” and “explicit” regularization, respectively. Usefully, these methods for 89
regularization do not require marginalizing across any coefficients, and are therefore much faster 90
than regularization in Bayesian or empirical-Bayes hierarchical models. Current NN methods 91
have also seen less use in fisheries science; one aim of the present paper is to promote the 92
exploration of these methods. Table 1 provides an explicit comparison between familiar concepts 93
in statistical-ecology and equivalent (though not always identical) concepts in neural 94
networks/artificial intelligence 95
Potential applications of Neural Networks in Fisheries 96
There are numerous types of neural network models, and this paper focuses on two for their 97
potential suitability to the spatial and/or temporal dynamism common to marine fisheries. 98
Recurrent Neural Networks (RNNs) are a subtype of neural network designed to handle 99
sequential data such as time series using feedback loops that maintain an internal state or 100
memory of previous inputs in the series. This recurrent structure enables RNNs to capture 101
temporal dependencies and model the evolution of dynamical systems. They are natural 102
candidates for nonlinear autoregressive models, where future values are predicted based on past 103
values. 104
105
However, basic RNNs can suffer from the numerical underflow or overflow issues (see Table 1) 106
during training, which makes it difficult for them to learn long-range dependencies in the data. 107
Long Short-Term Memory (LSTM) networks are a specialized type of RNN architecture 108
designed to mitigate these issues. LSTMs introduce a cell state, which acts as a long-term 109
memory, and sub-states known as “gates” that control the flow of information into and out of the 110
cell state, allowing the network to selectively remember and forget information over long 111
sequences. The value of RNNs like LSTMs lies in their ability to model and predict the behavior 112
of partially observed dynamical systems, where not all relevant state variables are directly 113
measured. By learning the temporal patterns in the observed data, RNNs can make predictions 114
about future states, which is highly valuable in fisheries science for forecasting population 115
dynamics, catch, and other time-dependent variables. 116
117
Convolutional Neural Networks (CNNs) were developed for the computer vision field as a 118
technique to facilitate the detection and labeling of images. In the simplest case, this involves a 119
multi-step process of passing (“convolving”) a set of learnable convolutional filters, or kernels, 120
to iteratively extract patterns. This process builds a hierarchical numerical representation, often 121
referred to as a feature map or embedding, that captures high-level features at low spatial 122
resolution. This allows the CNN to effectively learn spatial dependencies and patterns in the 123
image, which could be a photograph of an animal or a map of observed biomass from a fishery 124
independent survey, presenting an intriguing possibility for the standardization of spatially-125
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3
explicit data. However, the basic CNN framework is not designed to explicitly handle temporal 126
data nor irregular or sparse datasets characteristic of most fisheries surveys or catch time series. 127
Researchers have combined CNN and LSTM neural network approaches to produce forecasts of 128
spatial processes (e.g., Yang et al., (2025); the authors are aware of a single example wherein 129
CNN and LSTM neural network approaches were combined to produce forecasts of probable 130
catches (Agmata and Guðmundsson, 2025), although other studies have used CNN in isolation 131
(Morand et al., 2024). Crucially, that example did not conduct an explicit comparison between 132
the proposed CNN+LSTM approach, variations thereof, and currently-used methods for handling 133
spatio-temporal data, such as design-based expansion or regression-based standardization tools 134
such as tinyVAST, which we do in this case study. 135
Aims and Structure of this Paper 136
This "Food for Thought" paper introduces and applies these neural network approaches, both 137
alone and in combination, as a forward-looking demonstration for several foundational topics in 138
fisheries science: 1) the forecasting of population processes, with size-at-age as an example; 2) 139
the standardization of spatio-temporal indices of relative abundance, and 3) the discovery of 140
harvest policies to optimize catches and maintain spawning biomass. For each case study we 141
describe the methods used to produce the illustrative example, and discuss the relevance for the 142
fisheries assessment and management audience. Where possible, we provide direct mapping 143
between existing concepts in statistical ecology (such as spatio-temporal standardization or 144
interpolation) or fisheries management (such as management strategy evaluation, MSE; for this 145
reason, the section on reinforcement learning for management is longer than the others). 146
Advancing these techniques could enhance the adaptability, precision and sustainability of 147
scientific fisheries management in a rapidly changing environment. The paper concludes with a 148
“Research Roadmap” outlining the most important research questions to be considered in 149
evaluating the tractability of these tools for fisheries management in the coming decades. 150
151
Case Studies 152
This paper presents three case studies. Each is designed to highlight how NNs may be applied to 153
a variety of data types and processes central to fisheries management science. We also selected 154
these to represent a spectrum of tractability and impact, ranging from applications that could be 155
implemented today to those that would require completely novel management frameworks 156
Figure 1. We emphasize that the case study methods are examples and are not final; more work 157
is needed by the fisheries science community to investigate the tradeoffs, specifications, and 158
nuances of each application before they are ready for operational use. 159
160
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Case Study 1: Neural Networks for Stock Demography Forecasting 161
Even highly complex stock assessment models typically resort to simplification of observed 162
demographic processes in order to make management decisions. In particular, projections of 163
future size-at-age form the basis for fisheries management advice, yet scientists will commonly 164
use a historical or recent (e.g. 5-year) mean of observed fish sizes, though size-at-age can change 165
dramatically among years (Stawitz et al., 2019). Stock assessment models also rely on estimates 166
of historical size-at-age to derive estimates of historical biomass. Process-based models, such as 167
the von-Bertalanffy growth curve, are commonly used for estimating average size-at-age. Given 168
that size-at-age is well-observed for many managed fisheries, is sensitive to stochastic 169
environmental processes, and underpins catch advice for industrial fisheries management, this 170
case study illustrates how NN can provide flexibility to predict observable processes in fisheries. 171
172
We specifically compared the performance of two NN approaches to several existing methods 173
for deriving size-at-age. The models included a simple average of size-at-age from the terminal 174
five years of data (‘mean-5’), a three parameter von-Bertalanffy curve (‘VBGF’); a three 175
parameter von-Bertalanffy curve with IID year univariate random effects on asymptotic size and 176
growth rate (VBGF-RE’); a von Bertalanffy curve with 3D AR1 year, age, and cohort random 177
effects (‘GMRF’; Cheng et al., 2023); a simple 3-layer NN (‘NN’), and a LSTM (‘LSTM’); see 178
Supplementary Material S.1. for further details.. 179
180
To explore whether the relative performance of the different approaches depend on the temporal 181
structure of the simulation, we fit all six models to two simulated size-at-age datasets with 182
parameters based on Bering Sea pollock (Gadus chalcogrammus) from NOAA’s Alaska 183
Fisheries Science Center. The first simulated dataset simulated data from a three parameter von-184
Bertalanffy curve representing constant time-invariant growth. The second simulated dataset 185
simulated data from a three parameter von-Bertalanffy curve with time-varying parameters 186
following an AR1 and directional trend representing time-varying growth. Model parameters and 187
sample sizes used for simulated data-sets were based on sampling effort and life history 188
parameters of cod like species. We produced 300 30-year replicates of each dataset. Only 189
simulations in which all models converged were retained. 190
191
We evaluated prediction performance on each dataset by calculating the average root mean 192
squared error (RMSE) across ages from a 10-fold cross validation where random years of data 193
were removed from each fold. One- and two-year projection performance was evaluated using 194
five retrospective forecast peels. This allowed us to compare average RMSE across peels, both 195
for hindcast and projection accuracy and between the time-invariant or time-dependent scenarios. 196
197
This simulation exercise demonstrated that the LSTM most frequently resulted in the lowest 198
RMSE for all three prediction periods (hindcast, one and two years forward) for the time-199
invariant growth simulations (Figure 2). When simulated size-at-age varied through time, 200
average RMSE was most frequently lowest for the GMRF model for the hindcast and one-year 201
projection (Figure 2), though the LSTM and mean-5 performed comparably or better for the 202
two-year projection in this scenario. 203
204
The GMRF is designed to handle temporal variation explicitly and is able to separate observation 205
uncertainty from the latent temporal variability; it is possible that with lower observation error 206
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the performance of the LSTM method would have been improved. For both size-at-age 207
scenarios, we also visualized how predictive performance varied across ages, which had a less 208
distinct pattern (Supplementary Figures S1 and S2). 209
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Case Study 2: Standardizing survey data through space and time using a convolutional 210
neural network 211
Several methods have been developed to model or standardize for spatio-temporal processes in 212
fisheries data, particularly survey observations. These methods arose from the recognition that 213
underlying population processes and the methods for observing fish populations are subject to 214
variation in space and time, and accounting for this variation is required to ensure unbiased 215
estimates of population size or trajectory. The tinyVAST framework (Thorson et al., 2025) 216
builds upon the Vector Autoregressive Spatio-Temporal (VAST, Thorson (2019)) modeling 217
approach that allows users to specify separable Gaussian Markov Random fields and delta-218
GLMMs. The latest approach allows the specification of a broader class and flexibility of 219
multivariate models including spatial factor analysis and ARIMA (Jenkins, 2014) structures, 220
enabling the representation of simultaneous, lagged and recursive dependencies common to 221
ecological and fishery processes. TinyVAST is similar to sdmTMB (Anderson et al., 2022) in 222
that they both utilize the modern Template Model Builder language (Kristensen et al., 2016), 223
incorporate SPDE-based spatial precision matrices, though the former is better suited for 224
allowing for multivariate temporal dependencies. Surprisingly, the recognition that neural 225
network models are useful for data with strong spatial dependencies (Wikle and Zammit-226
Mangion, 2023) has not yet led to rigorous investigation of how these techniques compare to 227
existing approaches for standardizing biomass observations into annual indices of fishery 228
abundance. 229
230
The simulation study was conducted on a 20 x 20 spatial grid over 12 years, with spatial 231
correlation modeled through a row-standardized neighborhood matrix (rho = 0.95) and temporal 232
correlation through an AR1 process (p = 0.8). The underlying simulated biomass included both 233
spatial and temporal random effects; in each year 200 cells (50% of the domain) were randomly 234
sampled for observation that arose from a Tweedie distribution (Zainol Mustafa and Nadia, 235
2025; rho = 1.5, psi = 0.2). The experiment was replicated 25 times to assess model performance 236
and stability. For each replicate, observed data were passed to two CNN-based models 237
(described below) as well as to tinyVAST to a) interpolate continuous spatio-temporal biomass 238
estimates and b) calculate annual indices of abundance. A design-based estimator was included 239
for comparison for the annual indices. Design-based expansion is a simple calculation that takes 240
the average observation across sampled cells and multiplies it across the entire domain based on 241
the fraction of observed cells; this precludes the production of continuous surfaces but facilitates 242
comparison of annual indices. 243
244
We included two versions of the CNN approach, which differed in their handling of missing data 245
and temporal dependencies. Both approaches relied on the network to learn spatial relationships 246
through coordinate embeddings and produced continuous surfaces of estimated biomass. The 247
simpler approach, labeled “CNN” in results, took spatial coordinates as input and processed each 248
year separately; only points with observed (sampled) data were included in training. These 249
vectorized inputs passed through two dense embedding layers (dimensions 64 and 128, with 250
swish activation), reshaped to a 16x4x2 spatial tensor and processed by two 3x3 two-dimensional 251
convolutional layers with ReLU activation. The second approach, labeled “CNN-LSTM” 252
explicitly handled sparsity in the observed data via a binary masking channel which informed the 253
model where observations existed in a given year. Temporal information in the CNN-LSTM was 254
incorporated via a lag-based approach, whereby predictions at each timestep were informed by 255
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the previous three years of data. Both CNN models were implemented in R using the keras3 256
package (Kalinowski et al., 2025), compiled with Adam and a trainable Tweedie loss function 257
with sigmoid power parameter initialized to 1.5 and constrained to (1, 2) specified to support 258
comparison with tinyVAST. The 12-year, 25-repliate experiment to fit the three models took 16 259
hours to run on a personal computer. Performance was compared across models by examining 260
the trajectory of standardized indices, and overall RMSE in log-biomass and log-density (across 261
all replicates and years). 262
263
This simulation exercise demonstrated that neither of the CNN-based models out-performed the 264
existing tinyVAST approach in terms of log-biomass and log-density, though all approaches 265
were able to produced standardized indices of similar scale to the true biomass (Figure 3). recent 266
work has replicated our finding that CNNs can match, but not surpass, traditional species 267
distribution modeling approaches (Kellenberger et al., 2026). Examination of the interpolated 268
map for a single year and replicate shows that while both CNN-based models were able to 269
identify areas of relatively higher and lower biomass only tinyVAST was able to recover small-270
scale regional patterns. This application of CNNs certainly extends beyond the traditional 271
implementation, wherein an intact image (or collection of images for training) would be passed 272
to the model. CNNs are known to perform poorly when images are incompletely observed 273
(Heinke et al., 2021), and are also known to perform poorly when training data are limited (most 274
CNNs are trained on thousands of images, not 12 years of data as in this case) 275
276
There are promising applications of neural networks that could be used for the detection of 277
spatial patterns, some of which are in active development (e.g., (Deng et al., 2025)) and would 278
likely require the generation of continuous spatio-temporal loadings from observed data. 279
However, this case study indicates that tinyVAST is an appropriately precise and efficient 280
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https://doi.org/10.24127/sciencestatistics.v3i1.8003 569
570
571
572
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Tables 573
574
Term in statistical ecology Term in neural networks Brief description
deterministic latent variable layer A hidden but non-random
state predicted from the
model
nonlinear transformation for
element of a latent variable
neuron A method of abstraction to
map unobserved effects to
responses, for example,
through logistic or
exponential curves
reverse-mode automatic
differentiation
backpropagation Algorithm to efficiently
compute gradients by
working backwards through
the model
parameter weight A model value controlling the
strength of an input's effect
parameter estimation training The process of adjusting
parameters or weights to
minimize error on observed
data
regression modelling supervised learning Predicting outcomes from
inputs using observed data
gradient-based optimizer2 Stochastic gradient descent
(e.g., Adam)
Methodology for updating
model parameters during
training to minimize error
optimizing a management
policy
stochastic policy ascent A process of adjusting policy
parameters to optimize a
specific reward function
numerical overflow and
underflow
Exploding or vanishing
gradient
Because the gradient
calculation involves products
of terms, and each term in the
product might be very large
or small, the gradient might
2 Where each optimization step is based on a subset of data; hyperparameters control how the
explored parameters update given the gradient, and each loop through all partitions of the data is
called an “epoch”
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end up being smaller or larger
than the numerical minimum
or maximum allowed. This
can preclude accurate
calculation of the gradient.
575
Table 1. Non-exhaustive correspondence of vocabulary from statistical ecology to neural 576
network/AI methods. 577
578
579
Reinforcement Learning for
Fisheries
Management Strategy
Evaluation
Representation of
population/system dynamics
Operating model conditioned
to historical data, termed
“environment”
Operating model conditioned
to historical data
Data source used for model
selection
Future simulation or historical
data
Always future simulation
Representation of future
stochasticity
Simulated variation in future
recruitment deviations
Simulated variation in future
population processes,
typically recruitment
deviations
Representation of
observation and/or
estimation uncertainty
Can be addressed with
specialized neural network
architectures (i.e.,
environmental uncertainty as
hidden state)
Handled explicitly by
estimation model
How catches are selected The policy function, which is
learned from direct
interactions with the
environment, prescribes the
annual catch according to the
observed state
Pre-defined harvest control
rule sets annual catches based
on the current state (which
may be one or more estimated
quantities or observed data)
How performance is
measured
reward function is maximized
during training as the agent
interacts with the
environment; performance
metrics can be calculated after
training based on the
operating model time series,
After simulations, calculate
performance metrics using
operating model time series
during projection period
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as in MSE
Comparison across policies Harvest policies compared
internally as part of learning.
Novel harvest control rules
explored and evaluated; can
consider distinct yet flexible
rules; no consideration of
estimation models
Can consider distinct yet pre-
defined harvest control rules
and/or estimation models as
strategy components
Table 2. Comparison of key concepts in reinforcement learning-based policy discovery and 580
Management Strategy Evaluation. 581
582
583
For use in projections and management modeling
● Does including neural-network derived projections of weight-at-age improve
management performance? Can these approaches be extended to other key population
dynamics (i.e., numbers at age of recruitment?)
● Neural networks are not natively designed to handle nor represent uncertainty in their
predictions, which is something highly valued by the fishery management community
and often a requirement of reporting. How should we represent uncertainty in
projection models that use neural networks to project one or more components?
● If a neural network can predict data almost perfectly, how closely must that data
represent the system for the predictions to be acceptable for management?
● Is it possible to construct a neural network that predicts stock biomass using a feature
array of input data more accurately than a process-based estimation model?
● If so, can such a model be used to explore the impacts of varying catch levels on future
population biomass (and thus fully replace the process-based projection framework
used to calculate management quantities)?
● Can neural networks support the simulation component of management strategy
evaluation, perhaps enhancing the accuracy of predicted population dynamics,
observed data, or both?
For use in quota setting
● Can the data predicted by a neural network replace true observational data for short-
term management use (for example, to inform an empirical harvest control rule in the
absence of a survey), and if so, how long is “short term”?
● How might a management system integrate processed-based models with RL-derived
policies? At what frequency would operating models/environments need to be updated
to confidently rely upon a policy learned by RL?
● How would the development of RL-based policies be communicated to the fishery
community, and how would stakeholder engagement change under this paradigm?
For the fisheries science community
● Are there historical, social or economic characteristics of a fishery and management
system that are not well suited for these applications?
● What are the ethical considerations of providing management advice based on AI
models that inherently offer less explainability than existing methods?
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Table 3: List of questions arising from case studies, that could form the basis of future research 584
in scientific fisheries management. 585
586
587
588
589
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Figures 590
591
592
593
Figure 1. Conceptual diagram of case studies. The case studies were selected and are ordered 594
(from left to right) in terms of how tractably each NN application could be included in current 595
scientific fishery management frameworks. 596
597
598
Figure 2. Case Study 1: Number of times each process- and neural network based model resulted 599
in the lowest average root mean squared error (RMSE) when fit to simulated data (n = 300) 600
without (top row) or with (bottom row) a temporal trend in true fish growth. Hindcast represents 601
10-fold leave year out cross-validation and “y+1” and “y+2” represents forecast skill from 602
sequential peels of historical data and forecasted for two future years. 603
12
ed
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604
Figure 3. Case Study 2: Investigation of neural networks for spatio-temporal survey data 605
interpolation and index standardization. A) Mean scaled annual indices (lines) and 95% 606
confidence interval (shaded ribbon) for 25 replicates of a simulated 12-year biomass time series; 607
black solid line is true biomass whereas all other colors are model estimates. B) Performance 608
metrics of various estimation models (colors) in terms of RMSE in biomass (lefthand figure) or 609
density (righthand side) for estimates in a 20x20 gridded domain for 12 simulated years across 610
25 replicates. C) Maps of true and estimated log biomass across the domain for a single replicate 611
and year; results shown only for models that produce an interpolated surface as part of the 612
estimation step. 613
614
13
s;
te
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14
615
Figure 4. Case Study 3: Investigation of neural-network based reinforcement learning method 616
(orange lines and points) for fisheries management, in comparison to 25 replicates of an MSE 617
(blue lines and points) for EBS pollock using an OM conditioned on observations from 1964-618
2024 (grey rectangle; years are compressed) with a projection period from 2025-2050. Top row: 619
realized catch (millions of mt) under the constant (1a) and Ricker (1b) recruitment scenarios. 620
Middle row: stock spawning biomass in the operating model under the constant (2a) and Ricker 621
(2b) recruitment scenarios. Horizontal dashed line indicates 20% of unfished biomass and the 622
colored line represents the median across simulation replicates for a given year. Colored ribbons 623
represent 95% simulation interval. Bottom row: realized harvest policy in terms of the quota 624
(millions of mt) specified for future years(s) (points) versus the observed Bottom Trawl Survey 625
Biomass (t) arising from each method under the constant (3a) or Ricker (3b) recruitment 626
scenarios. The MSE did not use a survey-based method for setting quotas, but observations from 627
25 MSE replicates and the subsequent years’ catch are shown for comparison. 628
629
14
m
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105 and is also made available for use under a CC0 license.
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